By Agence France-Presse
However, while the week has got off to a positive start, there are lingering worries about a possible global trade war after the US hit Canada, Mexico and the European Union with steel and aluminium tariffs.
Focus is turning to a Group of Seven summit in Quebec later in the week, where US President Donald Trump is expected to go head-to-head with other world leaders over the levies, while China has warned Washington off imposing any measures against it.
The EU and Canada have filed complaints at the World Trade Organization, while the US Treasury Secretary faced severe criticism at a G7 finance ministers' gathering at the weekend.
All three main indexes on Wall Street ended sharply higher Friday after data showed the US created more jobs than expected in May, while the unemployment rate is at a near five-decade low. Separate figures showed US factory activity also beat estimates.
The gains in New York filtered through to Asia, where Tokyo ended 1.4 percent higher, while Hong Kong was also up 1.4 percent and Shanghai finished 0.5 percent higher.
Sydney rose 0.6 percent, Seoul gained 0.4 percent and Taipei put on 1.5 percent, with Singapore more than one percent higher.
In early European trade London rose 0.2 percent, Frankfurt added 0.9 percent and Paris was 0.6 percent higher.
The dollar also built on Friday's surge against the yen as the strong jobs report also lifted expectations for another interest rate hike by the Federal Reserve next week.
The euro held its gains after Italy's populist parties agreed to form a government, ending days of uncertainty that had fuelled fears of another election that would essentially be considered a referendum on its euro future.
A change of government in Spain also provided some support to the single currency, with the unpopular and corruption-plagued Mariano Rajoy replaced by Socialist Pedro Sanchez.
However, Stephen Innes, head of Asia-Pacific trading at OANDA, said: "With calm engulfing eurozone markets, the euro could find some relief over the short term but indeed the wear and tear from the election crisis, and the waves of populism gripping Europe, do point to some longer-term structural issues for the single currency."
Key figures around 0720 GMT
Tokyo - Nikkei 225: UP 1.4 percent at 22,475.94 (close)
Hong Kong - Hang Seng: UP 1.4 percent at 30,928.54
Shanghai - Composite: UP 0.5 percent at 3,091.19 (close)
London - FTSE 100: UP 0.2 percent at 7,718.90
Euro/dollar: UP at $1.1684 from $1.1659 at 2100 GMT on Friday
Pound/dollar: UP at $1.3370 from $1.3347
Dollar/yen: UP at 109.66 yen from 109.50 yen
Oil - West Texas Intermediate: DOWN five cents at $65.76 per barrel
Oil - Brent Crude: DOWN 27 cents at $76.52 per barrel
New York - Dow Jones: UP 0.9 percent at 24,635.21 (close)